How to add edge in a cylinder so that only the end can be scaled?
You can either add a loop cut, or cut the cylinder with the knife tool, or move your current end and extrude another edge to make it longer.

CtrlR is the keyboard shortcut for adding a loopcut.

To add a loop cut simply press CtrlR then LMB  (to confirm the count of one new edge) then move the edge down to the end and LMB  again to confirm the spot.  





K is for the knife tool.

To use the knife tool you are going to want to press 
Z after you started the knife tool, to enable "Cut through." Then after you made the cut press Enter or Space to confirm and leave the knife tool.





To extrude a new edge, first select your current end now press GG for the edge slide tool, move the end to where the taper starts.

A little trick to get the new extrusion along the same normal, press F to create a face. From that face blender will be able to continue the next extrusion along the exact same angle.

Now press E to extrude a new edge, simply LMB  when it is in the correct spot.